Abstract

Optical spectropolarimeters can be used to produce maps of the surfacemagnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map the surfacemagnetic fields of forming solar-like stars, which are still contracting under gravity and are surrounded by a disk of gas and dust. Their large scale magnetic fields are almost dipolar on some stars, and there is evidence for many higher order multipole field components on other stars. The availability of new data has renewed interest in incorporating multipolar magnetic fields into models of stellar magnetospheres. I describe the basic properties of axial multipoles of arbitrary degree and derive the equation of the field lines in spherical coordinates. The spherical magnetic field components that describe the global stellar field topology are obtained analytically assuming that currents can be neglected in the region exterior to the star, and interior to some fixed spherical equipotential surface. The field components follow from the solution of Laplace’s equation for the magnetostatic potential.

Received 06 April 2010Accepted 21 December 2010Published online 15 April 2011

Acknowledgments:

This work was supported by the Science and Technology Facilities Council Grant No. ST/G006261/1. The author thanks the two referees for constructive comments, and Professor C.G. Gray (University of Guelph) for insightful comments and a detailed reading of the manuscript.

Article outline:I. INTRODUCTIONII. STELLAR MAGNETIC FIELDSIII. THE MAGNETIC FIELD COMPONENTS OF AXIAL MULTIPOLESA. The effects of stellar outflowsB. The magnetic field components with a source surfaceIV. EQUATION OF THE FIELD LINESA. Field line plotsV. SUMMARY